Can you share with us your mathematical sources for the subject of
nonlinear dynamics. What I have observed, in recent years, is that some
mathematical ideas are becoming popularized among intelligent laymen
without very much of the accompanying mathematics. "Chaos" is a case in
point. While I have no particular objection to this, per se, it would
seem to pose a problem for those who wish to carefully model evolutionary
processes with nonlinear dynamics. Also, who besides you are using
nonlinear dynamics to describe evolution? While mathematically trained, I
do not make sense of your phase space ideas in the present context. This
is not to suggest that I am skeptical of your ideas. I just don't
understand them, presently.
By the way, I have run all three of your compiled programs. They are good
fun, and do seem pretty interesting. But I can sympathize with those who
view them as something of a black box. I view them as *illustrative* of
what *might* be occurring with mutational processes. Skeptics like Jim
Bell might easily find them totally unconvincing. On the other hand,
those who find evolution easier to accept are likely to find your programs
more satisfying. Ideally, one would like to be able to close up the gap by
making the link between the real and modeled mutational processes as
clearly stated as possible.
Jim does have a point. Mathematics does allow a great deal of flexibility
for model building. While not all things are possible, there are lot of
possibilities that incorrectly describe reality. A good illustration can
be given in physics: What happens when Newton's inverse square law is
replaced by an "inverse cube law" in the gravitational equation? Nothing
that resembles reality. But it is no more than a mathematical model - and
one can easily illustrate its effects on the computer. But it is just the
wrong model. Nothing more.
A "proof" of a good model is that it makes good predictions. The inverse
square law certainly meets this test. At present, does any mathematical
model of evolutionary processes make good predictions?
Gordon Simons